Paper Citation Record · LEDGER

Multiset Metric Dimension of Binomial Random Graphs

As of 8 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2507.11686.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.11686 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:16:33.730389Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T12:43:11.445008Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

23 of 23 outbound references displayed

verified exact2
verified fuzzy19
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cc3f9f7d-b49a-4515-aa91-5916e49ca73b · outbound

This paper cites A note on multiset dimension and local multiset dimension of graphs.

Multiset Metric Dimension of Binomial Random Graphs A note on multiset dimension and local multiset dimension of graphs

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.807225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8a4619b0-a13b-4f7e-a17e-4e06ea2a84b9 · outbound

This paper cites Springer, 1998.

Multiset Metric Dimension of Binomial Random Graphs Springer, 1998

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.724061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 27bc0aac-9884-4f33-ab08-584a2c9a28b5 · outbound

This paper cites Metric dimension for random graphs.

Multiset Metric Dimension of Binomial Random Graphs Metric dimension for random graphs

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.609497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f6cacc6c-0e00-4318-a9ec-bbe02b0cd25b · outbound

This paper cites Some properties of the multiset dimension of graphs.

Multiset Metric Dimension of Binomial Random Graphs Some properties of the multiset dimension of graphs

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.520465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ad6dc1d5-2603-4a6f-aacb-810d7f956cdc · outbound

This paper cites The Metric Dimension of Sparse Random Graphs.

Multiset Metric Dimension of Binomial Random Graphs The Metric Dimension of Sparse Random Graphs

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:16:34.062455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e01ce1f6-bfad-4bdd-bef0-df34713bc69a · outbound

This paper cites Local- ization game for random graphs.

Multiset Metric Dimension of Binomial Random Graphs Local- ization game for random graphs

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.367231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a73f11cf-c015-4ee4-820b-debbb4280750 · outbound

This paper cites A note on the localization number of random graphs: diameter two case.

Multiset Metric Dimension of Binomial Random Graphs A note on the localization number of random graphs: diameter two case

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.261107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0a514632-3c32-4152-87b3-119ad9da0324 · outbound

This paper cites An introduction to probability theory and its applications , volume 1.

Multiset Metric Dimension of Binomial Random Graphs An introduction to probability theory and its applications , volume 1

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.111618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eba66213-8970-4940-ac9a-03987cdb044b · outbound

This paper cites Cambridge University Press, 2016.

Multiset Metric Dimension of Binomial Random Graphs Cambridge University Press, 2016

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:36.030553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eea3fa61-21ed-4239-bb6e-9704718d2baf · outbound

This paper cites Distance-based vertex identification in graphs: The outer multiset dimension.

Multiset Metric Dimension of Binomial Random Graphs Distance-based vertex identification in graphs: The outer multiset dimension

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:35.857969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 512df7b3-8878-4236-92d8-ef8277cba2f6 · outbound

This paper cites Complexity and equivalency of multiset dimension and id-colorings.

Multiset Metric Dimension of Binomial Random Graphs Complexity and equivalency of multiset dimension and id-colorings

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:35.757505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8239f1f4-0a15-4ba9-88fc-15a96889fb77 · outbound

This paper cites Harary and R.A.

Multiset Metric Dimension of Binomial Random Graphs Harary and R.A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:35.596656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b166548f-a89d-41d8-a404-d29c62384f40 · outbound

This paper cites John Wiley & Sons, 2011.

Multiset Metric Dimension of Binomial Random Graphs John Wiley & Sons, 2011

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:35.498506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ce299033-2164-4d26-a021-194548bd90c1 · outbound

This paper cites Further contributions on the outer multiset dimension of graphs.

Multiset Metric Dimension of Binomial Random Graphs Further contributions on the outer multiset dimension of graphs

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:35.407458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5dfcedea-d9e7-4b62-b89c-bf7faa676ea3 · outbound

This paper cites Localization game for random geo- metric graphs.

Multiset Metric Dimension of Binomial Random Graphs Localization game for random geo- metric graphs

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:35.292899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation be2d6ff7-5435-46e4-80f4-40bfa061d549 · outbound

This paper cites On the limiting distribution of the metric dimension for random forests.

Multiset Metric Dimension of Binomial Random Graphs On the limiting distribution of the metric dimension for random forests

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:35.145219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 29237bfb-e312-4dec-96dc-551c37835b0b · outbound

This paper cites The role of adaptivity in source identification with time queries.

Multiset Metric Dimension of Binomial Random Graphs The role of adaptivity in source identification with time queries

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:34.941953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c014154a-ff85-494e-9489-833848f9c796 · outbound

This paper cites Sequential metric dimension for random graphs.

Multiset Metric Dimension of Binomial Random Graphs Sequential metric dimension for random graphs

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:34.795956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1f467cf9-1dcb-4344-ba43-c5b172281ccb · outbound

This paper cites The multiset dimension of graphs.

Multiset Metric Dimension of Binomial Random Graphs The multiset dimension of graphs

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T17:16:33.482803Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a949c73-bcab-4a58-b715-b030cf20c40a · outbound

This paper cites an unresolved cited work.

Multiset Metric Dimension of Binomial Random Graphs Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:16:34.634668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4a84bb6b-1660-40fa-92d6-2cf31c14881f · outbound

This paper cites Getting the lay of the land in discrete space: A survey of metric dimension and its applications.

Multiset Metric Dimension of Binomial Random Graphs Getting the lay of the land in discrete space: A survey of metric dimension and its applications

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:34.430680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fadd0e9b-176f-45c8-9ce0-f39b540bba5f · outbound

This paper cites Low-dimensional representation of genomic sequences.

Multiset Metric Dimension of Binomial Random Graphs Low-dimensional representation of genomic sequences

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:16:34.233240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1445ef30-58f0-492c-a204-e96305f8298c · outbound

This paper cites Multilateration of Random Networks with Community Structure.

Multiset Metric Dimension of Binomial Random Graphs Multilateration of Random Networks with Community Structure

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:16:33.911093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation b4a94524-3178-47ce-902e-75b2404d7aad · inbound

Multiset resolvability parameters in graphs: A survey with new results and open problems cites this paper.

Multiset resolvability parameters in graphs: A survey with new results and open problems Multiset Metric Dimension of Binomial Random Graphs

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-14T12:43:11.445008Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.